Examples of Minimal \(\varvec{G}\)-structures

  • Kamil Niedziałomski
Open Access


Let M be an oriented Riemannian manifold and SO(M) its oriented orthonormal frame bundle. Assume there exists a reduction \(P\subset SO(M)\) of the structure group \(SO(\dim M)\) to a subgroup G. We say that a G-structure M is minimal if P is a minimal submanifold of SO(M), where we equip SO(M) in the natural Riemannian metric. We give non-trivial examples of minimal G-structures for \(G=U(\dim M/2)\) and \(G=U((\dim M-1)/2)\times 1\) having some special features—locally conformally Kähler and \(\alpha \)-Kenmotsu manifolds, respectively.


G-structure intrinsic torsion minimal submanifold locally conformally Kähler manifold \(\alpha \)-Kenmotsu manifold 

Mathematics Subject Classification

53C10 53C25 53C43 



I wish to thank anonymous referee for many suggestions that led to improvement of the paper.


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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of ŁódźLodzPoland

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